Transcript What is capital budgeting?

What is capital budgeting?
Analysis of potential additions to
fixed assets.
Long-term decisions; involve large
expenditures.
Very important to firm’s future.
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Steps
1. Estimate CFs (inflows & outflows).
2. Assess riskiness of CFs.
3. Determine k = WACC (adj.).
4. Find NPV and/or IRR.
5. Accept if NPV > 0 and/or IRR >
WACC.
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What is the difference between
independent and mutually exclusive
projects?
Projects are:
independent, if the cash flows of
one are unaffected by the
acceptance of the other.
mutually exclusive, if the cash flows
of one can be adversely impacted
by the acceptance of the other.
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An Example of Mutually Exclusive
Projects
Firm owns one corner lot,
then it can build a gas
station or an apartment
building, but not both.
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Normal(Conventional) Cash Flow Project:
Cost (negative CF) followed by a
series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative
CF), then string of positive CFs,
then cost to close project.
e.g. Nuclear power plant
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Inflow (+) or Outflow (-) in Year
0
1
2
3
4
5
N
-
+
+
+
+
+
N
-
+
+
+
+
-
-
-
-
+
+
+
N
+
+
+
-
-
-
N
-
+
+
-
+
-
NN
NN
NN
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What is the payback period?
The number of years required to
recover a project’s cost,
or how long does it take to get our
money back?
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Payback for Project L
(Long: Large CFs in later years)
0
CFt
-100
Cumulative -100
PaybackL
= 2
+
1
2
10
-90
60
-30
30/80
2.4
3
80
50
= 2.375 years
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Project S (Short: CFs come quickly)
0
1
1.6 2
3
-100
70
50
20
Cumulative -100
-30
20
40
CFt
PaybackS
= 1 + 30/50 = 1.6 years
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Strengths of Payback:
1. Provides an indication of a
project’s risk and liquidity.
2. Easy to calculate and understand.
Weaknesses of Payback:
1. Ignores the TVM.
2. Ignores CFs occurring after the
payback period.
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Discounted Payback: Uses discounted
rather than raw CFs.
0
10%
1
2
3
10
60
80
CFt
-100
PVCFt
-100
9.09
49.59
60.11
Cumulative -100
-90.91
-41.32
18.79
Discounted
= 2
payback
+ 41.32/60.11 = 2.7 years
Recover investment in 2.7 years.
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NPV: Sum of the PVs of inflows and
outflows.
CFt
NPV  
t .
t  0 1  k 
n
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What’s Project L’s NPV?
Project L:
0
-100.00
10%
1
2
3
10
60
80
9.09
49.59
60.11
18.79 = NPVL
NPVS = $19.98.
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Calculator Solution
Enter CFs for L:
-100
CF0
10
CF1
60
CF2
80
CF3
10
I
NPV
= 18.78 = NPVL
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Rationale for the NPV Method
NPV = PV inflows – Cost
= Net gain in wealth.
Accept project if NPV > 0.
Choose between mutually
exclusive projects on basis of
higher NPV. Adds most value.
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Using NPV method, which project(s)
should be accepted?
If Projects S and L are mutually
exclusive, accept S because
NPVs > NPVL .
If S & L are independent,
accept both; NPV > 0.
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Internal Rate of Return: IRR
0
1
2
3
CF0
Cost
CF1
CF2
Inflows
CF3
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.
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NPV: Enter k, solve for NPV.
CFt

t  NPV .
t  0 1  k 
n
IRR: Enter NPV = 0, solve for IRR.
CFt

t  0.
t 0 1  IRR 
n
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What’s Project L’s IRR?
0
IRR = ?
-100.00
PV1
1
2
3
10
60
80
PV2
PV3
0 = NPV
Enter CFs , then press IRR:
IRRL = 18.13%. IRRS = 23.56%.
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Find IRR if CFs are constant:
0
IRR = ?
-100
INPUTS
2
3
40
40
40
3
N
OUTPUT
1
I/YR
-100
40
0
PV
PMT
FV
9.70%
Or enter CFs and press IRR = 9.70%.
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Q.
A.
How is a project’s IRR
related to a bond’s YTM?
They are the same thing.
A bond’s YTM is the IRR
if you invest in the bond.
0
1
2
IRR = ?
-1134.2
10
...
90
90
1090
IRR = 7.08% (using Fin. Calc.)
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Rationale for the IRR Method
If IRR > WACC, then the project’s
rate of return is greater than its
cost--some return is left over to
boost stockholders’ returns.
Example: WACC = 10%, IRR = 15%.
Profitable.
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IRR Acceptance Criteria
If IRR > k, accept project.
If IRR < k, reject project.
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Decisions on Projects S and L per IRR
If S and L are independent, accept
both. IRRs > k = 10%.
If S and L are mutually exclusive,
accept S because IRRS > IRRL .
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Construct NPV Profiles
Fin. Calc.: Enter CFs and find NPVL and
NPVS at different discount rates:
k
0
5
10
15
20
NPVL
50
33
19
7
(4
(4)
NPVS
40
29
20
12
5
25
NPV ($)
k
0
5
10
60
.
40 .
50
30
.
.
Crossover
Point = 8.7%
.
20
10
L
.
.
0
5
-10
10
15
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
S
.
.20
IRRS = 23.6%
.
Discount Rate (%)
23.6
IRRL = 18.1%
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NPV and IRR always lead to the same
accept/reject decision for independent
projects:
NPV ($)
IRR > k
and NPV > 0
Accept.
k > IRR
and NPV < 0.
Reject.
k (%)
IRR
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Mutually Exclusive Projects
k < 8.7: NPVL> NPVS , IRRS > IRRL
CONFLICT
k > 8.7: NPVS> NPVL , IRRS > IRRL
NO CONFLICT
NPV
L
S
k
8.7
k
IRRS
%
IRRL
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To Find the Crossover Rate
1. Find cash flow differences between
the projects. See data at beginning
of the case.
2. Enter these differences in CF
register, then press IRR. Crossover
rate = 8.68%, rounded to 8.7%.
3. Can subtract S from L or vice versa,
but better to have first CF negative.
4. If profiles don’t cross, one project
dominates the other.
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Reasons for conflict
Difference in project characteristics
1. Timing differences. Project with
faster payback provides more CF
in early years for reinvestment. If
k is high, early CF especially
good, NPVS > NPVL.
k
0
5
10
15
20
NPVL
50
33
19
7
(4)
NPVS
40
29
20
12
5
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Difference in assumption of NPV and IRR
Reinvestment Rate Assumptions
 NPV assumes reinvest at k (opportunity
cost of capital).
 IRR assumes reinvest at IRR.
 Reinvest at opportunity cost, k, is more
realistic, so NPV method is best. NPV
should be used to choose between
mutually exclusive projects.
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To see the reinvestment rate assumptions
Calculate average holding period return per year for projects
S and L using WACC and IRR as reinvestment rates.
WACC
5%
IRR
L
-100
10
60
80
S
-100
70
50
20
18.13%
23.56%
FV
FV
@wacc
@IRR
154.03
164.83
149.68
188.66
avg. hpr
@wacc
@IRR
15.49%
18.13%
14.39%
23.56%
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Managers like rates--prefer IRR to NPV
comparisons. Can we give them a
better IRR?
Yes, MIRR is the discount rate that
causes the PV of a project’s terminal
value (TV) to equal the PV of costs.
TV is found by compounding inflows
at WACC.
Thus, MIRR assumes cash inflows are
reinvested at WACC.
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MIRR for Project L (k = 10%)
0
1
2
3
10.0
60.0
80.0
10%
-100.0
10%
10%
MIRR = 16.5%
-100.0
PV outflows
$158.1
$100 =
(1 + MIRRL)3
66.0
12.1
158.1
TV inflows
MIRRL = 16.5%
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Why use MIRR versus IRR?
MIRR correctly assumes reinvestment
at opportunity cost = WACC. MIRR
also avoids the problem of multiple
IRRs.
Managers like rate of return
comparisons, and MIRR is better for
this than IRR.
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Consider projects S and L
Calculate MIRR and NPV of Projects S and L
at different rates of cost of capital
k
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
MIRR L
14.7%
14.9%
15.1%
15.3%
15.5%
15.7%
15.9%
16.1%
16.3%
16.5%
16.7%
16.9%
17.1%
17.3%
17.5%
MIRR S
12.4%
12.9%
13.4%
13.9%
14.4%
14.9%
15.4%
15.9%
16.4%
16.9%
17.4%
17.9%
18.4%
18.9%
19.4%
NPV L
46.37
42.86
39.48
36.21
33.05
30.00
27.06
24.21
21.45
18.78
16.20
13.70
11.28
8.94
6.67
NPV S
37.73
35.53
33.39
31.32
29.29
27.33
25.42
23.56
21.75
19.98
18.27
16.60
14.97
13.38
11.83
Thus, the use of MIRR accounts for timing differences.
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Project P: NPV and IRR?
0
-800
k = 10%
1
2
5,000
-5,000
Enter CFs in CF register, enter I = 10.
NPV = -386.78
IRR = ERROR. Why?
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We got IRR = ERROR because there
are 2 IRRs. Nonnormal CFs--two sign
changes. Here’s a picture:
NPV Profile
NPV
IRR2 = 400%
450
0
-800
100
400
k
IRR1 = 25%
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Logic of Multiple IRRs
1. At very low discount rates, the PV of CF2 is
large & negative, so NPV < 0.
2. At very high discount rates, the PV of both
CF1 and CF2 are low, so CF0 dominates and
again NPV < 0.
3. In between, the discount rate hits CF2
harder than CF1, so NPV > 0.
4. Result: 2 IRRs.
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When there are nonnormal CFs and
more than one IRR, use MIRR:
0
-800,000
1
5,000,000
2
-5,000,000
PV outflows @ 10% = -4,932,231.40.
TV inflows @ 10% = 5,500,000.00.
MIRR = 5.6%
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Accept Project P?
NO. Reject because MIRR =
5.6% < k = 10%.
Also, if MIRR < k, NPV will be
negative: NPV = -$386,777.
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Reasons for conflict:
Difference in project characteristics
2.
Size (scale) differences.
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Reasons for conflict
Difference in project characteristics
 If Big and Little are mutually exclusive projects,
which project should a firm prefer?
 If the firm goes strictly by the PI, IRR, or MIRR
criteria, it would choose Project Little.
 But is this the better project? Project Big
provides more value -- $89,299 versus $0.18.
The techniques that ignore the scale of the
investment such as IRR may lead to an incorrect
decision.
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